What shutter speed were you using? When photographin race cars I think I got my best panning shots are 1/250, but the speed of your subject will be a little bit slower, so I think maybe slow down your shutter a bit from 1/250 (or maybe the other way around?)

It varies. I put my aperature really small and put my camera on aperature priority mode so it would go to a low shutter speed. I think it was around 1/15 ?

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For a start ditch the tripod, set it to shutter priority because you want to control shutter speed not aperture, set your shutter speed to about 1/160, keep your elbows tight to your side as you pan and try not to move the camera up and down as you pan, once you get sharp shots of the car you can start to move you shutter speed down
This is at 1/40